
Back-scattering processes: diagram \((a)\)  in Fig.REF , are processes where a gravitational wave is emitted by the binary system and then reabsorbed into the same GW source. They are the lowest-order contributions to the effective action, but as we will show they do not affect the conservative dynamics, but they only contribute to the dissipative one.

Tail terms: diagram \((b)\)  in Fig.REF , are processes where a Gravitational Wave is emitted by the binary system and scattered off the quasi-static curvature into the same GW source. The dotted line denotes a graviton attached to a conserved charge, which imply that the corresponding Green's function has exactly zero time component momentum. They contribute to the conservative dynamics starting at 4PN as first noticed in [1]}, [2]}, and in the context of EFT in [3]}.

Memory terms: diagram \((c)\)  and \((d)\)  in Fig.REF , are processes where a GW is emitted by the binary system and scattered off the curvature induced by GW themselves. In that case all the gravitons are attached to dynamical multipoles, and we must pay attention in addressing their computation. They contribute to the conservative dynamics starting at 5PN as first noticed in [4]} in the context of linearized gravity, and then in [5]}. In order to distinguish between the two diagrams, we will refer to diagram \((d)\)  as double emission.

